Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors
GA Leonov, VA Boichenko - Acta Applicandae Mathematica, 1992 - Springer
This paper surveys results of the authors and others conceming estimates for the Hausdorff
dimension of strange attractors, particularly in the case of (generalized) Lorenz systems and …
dimension of strange attractors, particularly in the case of (generalized) Lorenz systems and …
[图书][B] Frequency-domain methods for nonlinear analysis: theory and applications
GA Leonov, DV Ponomarenko, VB Smirnova - 1996 - books.google.com
This book deals with the investigation of global attractors of nonlinear dynamical systems.
The exposition proceeds from the simplest attractor of a single equilibrium to more …
The exposition proceeds from the simplest attractor of a single equilibrium to more …
[图书][B] Attractor dimension estimates for dynamical systems: theory and computation
N Kuznetsov, V Reitmann - 2020 - Springer
In this book, we continue the investigations of global attractors and invariant sets for
dynamical systems by means of Lyapunov functions and adapted metrics. The effectiveness …
dynamical systems by means of Lyapunov functions and adapted metrics. The effectiveness …
[HTML][HTML] The Lyapunov dimension and its estimation via the Leonov method
NV Kuznetsov - Physics Letters A, 2016 - Elsevier
Along with widely used numerical methods for estimating and computing the Lyapunov
dimension there is an effective analytical approach, proposed by GA Leonov in 1991. The …
dimension there is an effective analytical approach, proposed by GA Leonov in 1991. The …
On RA Smith's autonomous convergence theorem
MY Li, JS Muldowney - The Rocky Mountain Journal of Mathematics, 1995 - JSTOR
RA Smith [19] showed that his higher dimensional generalization of Bendixson's criterion for
the nonexistence of periodic solutions to an autonomous differential equation implies that all …
the nonexistence of periodic solutions to an autonomous differential equation implies that all …
Lyapunov dimension formula for the global attractor of the Lorenz system
GA Leonov, NV Kuznetsov, NA Korzhemanova… - … in Nonlinear Science …, 2016 - Elsevier
The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of
parameters, including classical values, was analytically obtained first by GA Leonov in 2002 …
parameters, including classical values, was analytically obtained first by GA Leonov in 2002 …
Bounds for attractors and the existence of homoclinic orbits in the Lorenz system
GA Leonov - Journal of Applied Mathematics and Mechanics, 2001 - Elsevier
Frequency estimates are derived for the Lyapunov dimension of attractors of non-linear
dynamical systems. A theorem on the localization of global attractors is proved for the …
dynamical systems. A theorem on the localization of global attractors is proved for the …
Local Lyapunov exponents: looking closely at chaos
RCL Wolff - Journal of the Royal Statistical Society: Series B …, 1992 - Wiley Online Library
When a deterministic mechanism gives rise to an erratic time series, then under certain
conditions the series is said to exhibit chaos. The catalogue of statistical methods for the …
conditions the series is said to exhibit chaos. The catalogue of statistical methods for the …
An ultimate bound on the trajectories of the Lorenz system and its applications
AY Pogromsky, G Santoboni, H Nijmeijer - Nonlinearity, 2003 - iopscience.iop.org
In this paper, a new bound on the trajectories of the Lorenz system is derived. This result is
useful to show that the transverse stability of the origin in two Lorenz systems coupled in a …
useful to show that the transverse stability of the origin in two Lorenz systems coupled in a …
[图书][B] Reguläre und chaotische Dynamik
V Reitmann - 1996 - Springer
Dieses Lehrbuch basiert auf Ausarbeitungen zu verschiedenen Vorlesungen, die ich in den
Jahren 1989 bis 1996 an der TU Dresden gehalten habe. Zu den Hörern dieser …
Jahren 1989 bis 1996 an der TU Dresden gehalten habe. Zu den Hörern dieser …